Figure 2.

CNC natural stone processing machines.


#### Table 3.

Technical properties of CNC natural stone processing machine.

Natural stone samples were bond and stabilized to the platform on the measurement unit with cut tools. There were 4 on the Z axis, 4 on the X and Y axis total 8 load cells on the testing machine to calculate the Cf. Defne Lab-Soft program was recorded into the data input screen of types and sizes of natural rocks, cutter information, and constant and variable parameters. NC codes from Alphacam drawing program were transferred to the CNC machine with Recon program interface. The cut tool was balanced to the engine of the CNC machine connected to the tool holder. The reset operation was performed when the cutting tool was guided by the function and operation keys to the reference point on the test specimen surface. NC code was selected using the function and operation keys on the control unit and the measurement was performed by pressing the start button. Depending on the different process parameters, the natural stones were processed in the cooling process from the water flow rate of 1 l/min. A rectangle of 120 25 mm was processed for 40 s to obtain 100 data per second. All samples were processed in a total of 84 min. Figure 4 shows a schematic view of the test apparatus.

In the processability tests, variable and constant parameters were taken into consideration. Constant cutting parameters were the cut tool diameter of 6.0 mm, spindle speed of 10,000 d/min, cutting width of 3.0 mm and plunge speed of 1000 d/min. Variable cutting parameters were the dp of 1.20, 1.60 and 2.0 mm and Va of

Processability tests (a) vector representation of forces (Fx, Fy, Fc and Ft), cutting speed (Vt) and Va(Va), (b) power and load meter tester and load cells, (c) control unit, (d) Defne lab-soft natural stone test program

interface, (e) recon program interface, (f) views of database.

Test specimens on (a) alpha CAM drawing program, (b) modeling, (c) simulation.

Force and Specific Energy in Natural Rocks Cutting by Four-Axis Machine

DOI: http://dx.doi.org/10.5772/intechopen.85622

Figure 3.

Figure 4.

15

Force and Specific Energy in Natural Rocks Cutting by Four-Axis Machine DOI: http://dx.doi.org/10.5772/intechopen.85622

#### Figure 3. Test specimens on (a) alpha CAM drawing program, (b) modeling, (c) simulation.

#### Figure 4.

Natural stone samples were bond and stabilized to the platform on the measurement unit with cut tools. There were 4 on the Z axis, 4 on the X and Y axis total 8 load cells on the testing machine to calculate the Cf. Defne Lab-Soft program was recorded into the data input screen of types and sizes of natural rocks, cutter information, and constant and variable parameters. NC codes from Alphacam drawing program were transferred to the CNC machine with Recon program interface. The cut tool was balanced to the engine of the CNC machine connected to the tool holder. The reset operation was performed when the cutting tool was guided by the function and operation keys to the reference point on the test specimen surface. NC code was selected using the function and operation keys on the control unit and the measurement was performed by pressing the start button. Depending on the different process parameters, the natural stones were processed in the cooling process from the water flow rate of 1 l/min. A rectangle of 120 25 mm was processed for 40 s to obtain 100 data per second. All samples were processed in a

Technical properties/unit Values Spindle motor (kW) 9.0 Number of axis (number) 4.0 Motor speed (rpm) 24.000 Processing speed (rpm) 24.000 Vamotor x axis (mm/dk) 80.000 Voltage (V) 380 Processing length (mm) 4.000–4.500 Processing width (mm) 2.000–2.500 Processing height (mm) 500–600 Lathe height (mm) 700–750 Lathe length (mm) 2.500–3.000 Coolant (l/dk) 3.0 Automatic number of teams (adet) 8.0

total of 84 min. Figure 4 shows a schematic view of the test apparatus.

Technical properties of CNC natural stone processing machine.

Figure 2.

Earth Crust

Table 3.

14

CNC natural stone processing machines.

Processability tests (a) vector representation of forces (Fx, Fy, Fc and Ft), cutting speed (Vt) and Va(Va), (b) power and load meter tester and load cells, (c) control unit, (d) Defne lab-soft natural stone test program interface, (e) recon program interface, (f) views of database.

In the processability tests, variable and constant parameters were taken into consideration. Constant cutting parameters were the cut tool diameter of 6.0 mm, spindle speed of 10,000 d/min, cutting width of 3.0 mm and plunge speed of 1000 d/min. Variable cutting parameters were the dp of 1.20, 1.60 and 2.0 mm and Va of 2500, 3000, 3500 mm/min. Table 4 shows the CNC cutting parameters for the natural rocks processed in the tests.

Figure 5 explains the vector representation of the forces (Fx, Fy, Fc and Ft), Vt and Va that occurred during the processing of the natural rocks.

Calculation of Fx cutting force according to CNC processing parameters is as shown in Eq. (1).

Fx cutting force Eq. (1);

$$F\_{\mathbf{x}} = |F\_{\mathbf{x1}}| + |F\_{\mathbf{x2}}| \tag{1}$$

<sup>β</sup> <sup>¼</sup> tan �<sup>1</sup> Fy

<sup>θ</sup> <sup>¼</sup> cos �<sup>1</sup> <sup>1</sup> � <sup>2</sup>dp

Calculating Fc tangential force and radial force Ft components of the cutting

Contact angle θ between tool diameter (d) and natural rocks, Eq. (5);

Force and Specific Energy in Natural Rocks Cutting by Four-Axis Machine

Parameter Z depends on the location of the application point of the compound forces R on the arc AC, which is contact between cutting edges and

<sup>Z</sup> <sup>¼</sup> AB

Vt <sup>¼</sup> <sup>π</sup> � <sup>D</sup> � <sup>n</sup>

Specific cutting energy depending on tangential force and cutting speed is

Sc <sup>¼</sup> Fc � Vt

Fc = tangential cutting force (N); Vt = cutting speed (m/min); Va = feed speed

Se values were calculated using the power P and Qw obtained from the main electric motor of 7.5 kW where the cutting end of the natural rocks was connected

Vt = cutting speed (m/min); n = spindle speed (d/min); D = cutter

(mm/min); dp = cutting depth (mm); b = cutting width (mm).

forces with the R value obtained.

DOI: http://dx.doi.org/10.5772/intechopen.85622

δ angle between Ft and Fc.

Parameter Z, Eq. (9):

Vt cutting speed Eq. (10):

during the processability time (t).

Qw = chip volume (mm3

17

The chip volume is shown in Eq. (12).

sample (mm); dp(1,2,3) = cutting depth (mm). The total specific energy is shown in Eq. (13).

Eqs. (6) and (7):

Eq. (8):

natural rocks.

diameter (mm).

shown in Eq. (11).

Fx

d

(4)

(5)

Fc ¼ Rsinδ (6) Ft ¼ Rcosδ (7)

δ ¼ β � Zθ (8)

AC (9)

<sup>1000</sup> (10)

Va � dp � <sup>b</sup> (11)

Qw ¼ b � l � dpð Þ 1; 2; 3 (12)

); b = size of the sample (mm); l = the width of the

Fx = cutting force (N); Fx1 = absolute forward cutting force (N); Fx2 = absolute back cutting force (N).

Fy cutting force Eq. (2);

$$F\_{\mathcal{Y}} = |F\_{\mathcal{Y}1}| + |F\_{\mathcal{Y}2}|\tag{2}$$

Fy = cutting force (N); Fy1 = absolute forward cutting force (N); Fy2 = absolute back cutting force (N).

Calculation by using R resultant force, Fx and Fy cutting forces, Eq. (3):

$$R = \sqrt{F\_x^2 + F\_y^2} \tag{3}$$

R = resultant force (N); Fx = cutting force (N); Fy = cutting force (N). β angle between R and Fx, Eq. (4),


#### Table 4.

CNC processing parameters.

Figure 5. Vector representation of the forces (Fx, Fy, Fc and Ft), Vt and Va that occur during the processing.

Force and Specific Energy in Natural Rocks Cutting by Four-Axis Machine DOI: http://dx.doi.org/10.5772/intechopen.85622

$$\beta = \tan^{-1} \left( \frac{F\_{\text{y}}}{F\_{\text{x}}} \right) \tag{4}$$

Contact angle θ between tool diameter (d) and natural rocks, Eq. (5);

$$\theta = \cos^{-1}\left(1 - \frac{2dp}{d}\right) \tag{5}$$

Calculating Fc tangential force and radial force Ft components of the cutting forces with the R value obtained.

Eqs. (6) and (7):

2500, 3000, 3500 mm/min. Table 4 shows the CNC cutting parameters for the

Vt and Va that occurred during the processing of the natural rocks.

Figure 5 explains the vector representation of the forces (Fx, Fy, Fc and Ft),

Calculation of Fx cutting force according to CNC processing parameters is as

Fx = cutting force (N); Fx1 = absolute forward cutting force (N); Fx2 = absolute

Fy = cutting force (N); Fy1 = absolute forward cutting force (N); Fy2 = absolute

� þ Fy<sup>2</sup> � � �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F2 <sup>x</sup> <sup>þ</sup> <sup>F</sup><sup>2</sup> y

Fy ¼ Fy<sup>1</sup> � � �

Calculation by using R resultant force, Fx and Fy cutting forces, Eq. (3):

q

R ¼

Vector representation of the forces (Fx, Fy, Fc and Ft), Vt and Va that occur during the processing.

R = resultant force (N); Fx = cutting force (N); Fy = cutting force (N).

Processing parameters Unit Values Cutting tool diameter mm 6.0 Depth of cut mm 1.20–1.60–2.00 Spindle speed d/min 10,000 Feed speed mm/min 2000–2500–3000 Plunge speed d/min 1000 Cutting speed m/min 188.4 Cutting width mm 3.0

Fx ¼ j j Fx<sup>1</sup> þ j j Fx<sup>2</sup> (1)

� (2)

(3)

natural rocks processed in the tests.

Fx cutting force Eq. (1);

Fy cutting force Eq. (2);

β angle between R and Fx, Eq. (4),

shown in Eq. (1).

Earth Crust

back cutting force (N).

back cutting force (N).

Table 4.

Figure 5.

16

CNC processing parameters.

$$F\_c = R \sin \delta \tag{6}$$

$$F\_t = R\cos\delta\tag{7}$$

δ angle between Ft and Fc. Eq. (8):

$$
\delta = \beta - \mathcal{Z}\theta \tag{8}
$$

Parameter Z depends on the location of the application point of the compound forces R on the arc AC, which is contact between cutting edges and natural rocks.

Parameter Z, Eq. (9):

$$Z = \frac{AB}{AC} \tag{9}$$

Vt cutting speed Eq. (10):

$$V\_t = \frac{\pi \times D \times n}{1000} \tag{10}$$

Vt = cutting speed (m/min); n = spindle speed (d/min); D = cutter diameter (mm).

Specific cutting energy depending on tangential force and cutting speed is shown in Eq. (11).

$$S\_c = \frac{F\_c \times V\_t}{V\_a \times d\_p \times b} \tag{11}$$

Fc = tangential cutting force (N); Vt = cutting speed (m/min); Va = feed speed (mm/min); dp = cutting depth (mm); b = cutting width (mm).

Se values were calculated using the power P and Qw obtained from the main electric motor of 7.5 kW where the cutting end of the natural rocks was connected during the processability time (t).

The chip volume is shown in Eq. (12).

$$Q\_w = b \times l \times dp(\mathbf{1}, \mathbf{2}, \mathbf{3})\tag{12}$$

Qw = chip volume (mm3 ); b = size of the sample (mm); l = the width of the sample (mm); dp(1,2,3) = cutting depth (mm).

The total specific energy is shown in Eq. (13).

$$\mathbf{S}\_{\epsilon} = \frac{\frac{\sum\_{j=1}^{n} \mathbf{P} \mathbf{j}}{n} \times \sum\_{j=1}^{n} \mathbf{t} \mathbf{j}}{Q\_{w(1,2,3)}} \tag{13}$$

Se = total specific energy (J/mm3 ); P = power consumption (W); t = total time (s); Qw = chip volume (mm3 ).

## 3. Findings and evaluations

#### 3.1 Petrographic, chemical and physicomechanical properties

The petrographic analysis was carried out in the MTA (General Directorate Mineral Research and Exploration) mineralogical and petrographic analysis laboratory in Ankara/Turkey. Chemical properties of natural rocks were performed using the XRF (X-ray fluorescence) method in ACME (Analytical Laboratory in Turkey/ Ankara). The metamorphic (marble) and sedimentary (travertine, and limestone) origin natural rocks used in this study had different textures. All natural rock types were composed of CaO as main calcite crystals and at least 99.0% calcite minerals ranging from 53.10 to 55.70%. The petrographic analysis results and chemical analysis of the samples are presented in Tables 5 and 6, respectively. Petrographic and chemical analysis results of samples are given in Tables 5 and 6, respectively.

The CNC processability tests were conducted in the Rock Mechanics and Technology Application and Research Center Laboratory of the Department of Mining Engineering of Afyon Kocatepe University. The tests were performed in accordance with Standard No. TS EN 1936: 2010 [41], Standard No. TS EN 13755: 2014 [42], Standard No. TS EN 14205: 2004 [43], Standard No. TS EN 1926: 2007 [44], Standard No. TS EN 13161: 2014 [45], Standard No. TS 699 [46] and Standard No. TS EN 1341 (Appendix-C: 2013) [47]. The physicomechanical properties of the natural rocks are presented in Table 7. The rock samples were 40 � 40 mm<sup>3</sup> , <sup>70</sup> � <sup>70</sup> � 70 mm<sup>3</sup> and 30 � <sup>50</sup> � 180 mm3 . The tests were carried out using at least six samples.

#### 3.2 Variance analysis (ANOVA) of cutting forces

In processability tests, the Fc and Ft measurements were conducted using twofactor analysis of variance (ANOVA) (17 natural rocks � 2 Cf � 3 dp � 3 Va) randomized experimental design with 100 replications (n = 100). A total of 30,600 data were obtained on the rocks. In terms of the Cf (Fc, Ft), among the dp and Va there was a statistically significant difference (P < 0.001) (Table 8).

randomized experimental design with 100 replications (n = 100). A total of 30,600 data were obtained on the rocks. In terms of the Sc and Se, among the dp and Va

K2 96% Calcite (mic),

K3 95% Calcite (mic),

K4 95% Calcite (mic),

K5 95% Calcite (mic),

Petrographic descriptions Minerals

T2 78% Calcite (mic),

T3 79% Calcite (mic),

T4 78% Calcite (mic),

T5 77% Calcite (mic),

M2 97.5% Calcite M3 98% Calcite M4 98.5% Calcite M5 98.5% Calcite M6 99% Calcite M7 97% Calcite, 2%

77% Calcite (mic), 22% Calcite (spr)

21% Calcite (spr)

20% Calcite (spr)

21% Calcite (spr)

22% Calcite (spr)

98.5% Calcite

dolomite

96% Calcite (mic), 2% Calcite (spr)

2% Calcite (spr)

3% Calcite (spr)

3% Calcite (spr)

3% Calcite (spr)

T1 Fine-grained calcite is the dominant mineral. Consist of micro-

Force and Specific Energy in Natural Rocks Cutting by Four-Axis Machine

DOI: http://dx.doi.org/10.5772/intechopen.85622

M1 Fine, medium, medium-coarse and coarse-grained with polysynthetic

K1 Fine-grained. Consists of cryptocrystalline calcite within crypto microcrystalline calcite. Micritic texture. Limestones

twins, granoblastic texture. Marbles

mesocrystalline calcite minerals with a little amount of clay. Often contains pores. Micritic (intraclast) texture. Travertines

In processability tests for natural rocks, the mean Sc and Se values at the dp of 1.2 mm are lower than those at the dp of 1.6 and 2.0 mm was given in Figure 7. Sc and Se values at the Va of 2000 mm/min are higher than those at the Va of 2500 and 3000 mm/min. Sc and Se values at the Va of 3000 mm/min are lower for T1, T2, and T3 samples while those at the Va of 2000 mm/min are higher for both K4 and K5 samples. The natural rocks should have the Va of 3000 mm/min according to the Sc

Regression models were applied to examine the relationship between the Cf and Sc values for each of the natural rocks. The results of the simple linear regression

there was a statistically significant difference (P < 0.001) (Table 9).

3.4 Relationships between cutting forces and specific cutting energy

and Se values.

19

Table 5.

Natural Rocks

analysis are given in Figure 8.

Petrographic descriptions of natural rock samples.

In processability tests for natural rocks, the mean Fc and Ft increase with an increase in the dp and Va was given in Figure 6. K4 and K5 samples have high values of the Cf at the dp of 2.0 mm while T1, T2, and T3 samples have low values of the Cf at the dp of 1.2 mm. Processability of the Cf values of K4 and K5 samples the dp of 2.0 mm is more forced than that of the other samples. K4 and K5 samples have high values of the Cf at a Va of 3.000 mm/min while T1, T2, and T3 samples have low values of the Cf at a Va of 2.000 mm/min. Processability of the Cf of K4 and K5 samples at a Va of 3.000 mm/min is more forced than that of the other samples.

#### 3.3 Variance analysis (ANOVA) of specific cutting energy and specific energy

In processability tests, the Sc and Se measurements were conducted using twofactor analysis of variance (ANOVA) (Sc and Se for 12 natural rocks � 3 dp � 3 Va)


#### Table 5.

Se ¼

3.1 Petrographic, chemical and physicomechanical properties

Se = total specific energy (J/mm3

<sup>70</sup> � <sup>70</sup> � 70 mm<sup>3</sup> and 30 � <sup>50</sup> � 180 mm3

3.2 Variance analysis (ANOVA) of cutting forces

six samples.

18

).

Qw = chip volume (mm3

Earth Crust

3. Findings and evaluations

∑<sup>n</sup> <sup>j</sup>¼1Pj <sup>n</sup> � <sup>∑</sup><sup>n</sup>

<sup>j</sup>¼1tj

); P = power consumption (W); t = total time (s);

(13)

,

. The tests were carried out using at least

Qwð Þ <sup>1</sup>;2;<sup>3</sup>

The petrographic analysis was carried out in the MTA (General Directorate Mineral Research and Exploration) mineralogical and petrographic analysis laboratory in Ankara/Turkey. Chemical properties of natural rocks were performed using the XRF (X-ray fluorescence) method in ACME (Analytical Laboratory in Turkey/ Ankara). The metamorphic (marble) and sedimentary (travertine, and limestone) origin natural rocks used in this study had different textures. All natural rock types were composed of CaO as main calcite crystals and at least 99.0% calcite minerals ranging from 53.10 to 55.70%. The petrographic analysis results and chemical analysis of the samples are presented in Tables 5 and 6, respectively. Petrographic and chemical analysis results of samples are given in Tables 5 and 6, respectively.

The CNC processability tests were conducted in the Rock Mechanics and Technology Application and Research Center Laboratory of the Department of Mining Engineering of Afyon Kocatepe University. The tests were performed in accordance with Standard No. TS EN 1936: 2010 [41], Standard No. TS EN 13755: 2014 [42], Standard No. TS EN 14205: 2004 [43], Standard No. TS EN 1926: 2007 [44], Standard No. TS EN 13161: 2014 [45], Standard No. TS 699 [46] and Standard No. TS EN 1341 (Appendix-C: 2013) [47]. The physicomechanical properties of the natural rocks are presented in Table 7. The rock samples were 40 � 40 mm<sup>3</sup>

In processability tests, the Fc and Ft measurements were conducted using two-

In processability tests for natural rocks, the mean Fc and Ft increase with an increase in the dp and Va was given in Figure 6. K4 and K5 samples have high values of the Cf at the dp of 2.0 mm while T1, T2, and T3 samples have low values of the Cf at the dp of 1.2 mm. Processability of the Cf values of K4 and K5 samples the dp of 2.0 mm is more forced than that of the other samples. K4 and K5 samples have high values of the Cf at a Va of 3.000 mm/min while T1, T2, and T3 samples have low values of the Cf at a Va of 2.000 mm/min. Processability of the Cf of K4 and K5 samples at a Va of 3.000 mm/min is more forced than that of the other samples.

3.3 Variance analysis (ANOVA) of specific cutting energy and specific energy

In processability tests, the Sc and Se measurements were conducted using twofactor analysis of variance (ANOVA) (Sc and Se for 12 natural rocks � 3 dp � 3 Va)

factor analysis of variance (ANOVA) (17 natural rocks � 2 Cf � 3 dp � 3 Va) randomized experimental design with 100 replications (n = 100). A total of 30,600 data were obtained on the rocks. In terms of the Cf (Fc, Ft), among the dp and Va

there was a statistically significant difference (P < 0.001) (Table 8).

Petrographic descriptions of natural rock samples.

randomized experimental design with 100 replications (n = 100). A total of 30,600 data were obtained on the rocks. In terms of the Sc and Se, among the dp and Va there was a statistically significant difference (P < 0.001) (Table 9).

In processability tests for natural rocks, the mean Sc and Se values at the dp of 1.2 mm are lower than those at the dp of 1.6 and 2.0 mm was given in Figure 7. Sc and Se values at the Va of 2000 mm/min are higher than those at the Va of 2500 and 3000 mm/min. Sc and Se values at the Va of 3000 mm/min are lower for T1, T2, and T3 samples while those at the Va of 2000 mm/min are higher for both K4 and K5 samples. The natural rocks should have the Va of 3000 mm/min according to the Sc and Se values.

### 3.4 Relationships between cutting forces and specific cutting energy

Regression models were applied to examine the relationship between the Cf and Sc values for each of the natural rocks. The results of the simple linear regression analysis are given in Figure 8.


#### Table 6.

Chemical characteristics of natural rock samples.


Figure 8 shows that there is a statistically significant relationship between Sc and

Fc at depths of cut of 1.2, 1.6 and 2.0 mm are 0.895, 0.871 and 0.859, respectively.

depths of cut of 1.2, 1.6 and 2.0 mm are 0.890, 0.878 and 0.880, respectively.

Va of 2000, 2500 and 3000 mm/min are 0.771, 0.780 and 0.780, respectively.

Va of 2000, 2500 and 3000 mm/min are 0.745, 0.781 and 0.781, respectively.

The results of the correlation coefficient and regression model are given in

3.5 Relationships between specific cutting energy and specific energy

indicating that there is a linear relationship between the Sc and Se.

) values obtained from the natural rocks in the

) values obtained from the natural rocks in the Ft at

) values obtained from the natural rocks in the Fc at the

) values obtained from the natural rocks in the Ft at the

) obtained from the natural rocks is 0.784,

Cf values. Correlation coefficient (R<sup>2</sup>

Statistical analysis of Cf of natural rocks depending on the dp and Va.

\*The mean difference is significant at the, 05 level.

Figure 9. Correlation coefficient (R2

Correlation coefficient (R2

Table 8.

21

Cf (N) dependent variable

Va(mm/dk)

dp (mm) Mean difference

Mean (J)

Force and Specific Energy in Natural Rocks Cutting by Four-Axis Machine

Mean (I)

DOI: http://dx.doi.org/10.5772/intechopen.85622

(I-J)

Fc 1.20 1.00 3.8214\* 0.27897 <0.001 4.4787 3.1642

Ft 1.20 1.60 3.7896\* 0.27690 <0.001 4.4420 3.1372

Fc 2000 2500 2.2064\* 0.27897 <0.001 2.8637 1.5491

Ft 2000 2500 2.1094\* 0.27690 <0.001 2.7618 1.4570

Std. Error

2.00 7.4694\* 0.27897 <0.001 81267 6.8122

2.00 3.6480\* 0.27897 <0.001 4.3052 2.9907

1.60 3.6480\* 0.27897 <0.001 2.9907 4.3052

2.00 7.5726\* 0.27690 <0.001 8.2250 6.9202

2.00 3.7830\* 0.27690 <0.001 4.4354 3.1306

1.60 3.7830\* 0.27690 <0.001 3.1306 4.4354

3000 3.7687\* 0.27897 <0.001 4.4259 3.1114

3000 1.5623\* 0.27897 <0.001 2.2195 0.9050

2500 1.5623\* 0.27897 <0.001 0.9050 2.2195

3000 3.3713\* 0.27690 <0.001 4.0236 2.7189

3000 1.2619\* 0.27690 <0.001 1.9142 0.6095

2500 1.2619\* 0.27690 <0.001 0.6095 19142

1.60 1.20 3.8214\* 0.27897 <0.001 3.1642 4.4787

2.00 1.20 7.4694\* 0.27897 <0.001 6.8122 8.1267

1.60 1.20 3.7896\* 0.27690 <0.001 3.1372 4.4420

2.00 1.20 7.5726\* 0.27690 <0.001 6.9202 8.2250

2500 2000 2.2064\* 0.27897 <0.001 1.5491 2.8637

3000 2000 3.7687\* 0.27897 <0.001 3.1114 4.4259

2500 2000 2.1094\* 0.27690 <0.001 1.4570 2.7618

3000 2000 3.3713\* 0.27690 <0.001 2.7189 4.0236

Sig. 95% confidence interval

Upper bound

Lower bound

Correlation coefficient (R2

Correlation coefficient (R2

D, density; P, porosity; WA, water absorption; KH, knoop hardness; UCS, uniaxial compressive strength; FS, flexural strength; IS, impact strength; AR, abrasion strength.

#### Table 7.

Physico-mechanical properties of natural rocks.


#### Force and Specific Energy in Natural Rocks Cutting by Four-Axis Machine DOI: http://dx.doi.org/10.5772/intechopen.85622

#### Table 8.

Natural Rocks

Earth Crust

Table 6.

Chemical characteristics of natural rock samples.

Natural Rocks D (kg/m<sup>3</sup>

IS, impact strength; AR, abrasion strength.

Physico-mechanical properties of natural rocks.

Table 7.

20

CaO (%)

SiO2 (%) Al2O3 (%)

Fe2O3 (%)

MgO (%)

T1 55.70 0.01 0.01 0.01 0.01 0.015 0.01 0.03 0.02 43.96 T2 55.44 0.06 0.01 0.02 0.06 0.11 0.01 0.02 0.03 44.02 T3 55.45 0.01 0.01 0.01 0.28 0.12 0.01 0.02 0.01 44.08 T4 55.47 0.01 0.01 0.01 0.21 0.10 0.01 0.02 0.01 44.01 T5 55.48 0.06 0.01 0.02 0.09 0.11 0.01 0.02 0.03 43.95 M1 55.59 0.01 0.01 0.01 0.11 0.21 0.01 0.04 0.01 44.00 M2 54.40 0.95 0.31 0.05 0.21 0.04 0.01 0.01 0.01 44.00 M3 54.16 0.89 0.27 0.09 0.81 0.08 0.02 0.01 0.04 43.60 M4 53.37 1.57 0.57 0.29 0.75 0.27 0.03 0.03 0.04 43.06 M5 55.38 0.17 0.03 0.09 0.31 0.21 0.01 0.02 0.01 43.76 M6 55.08 0.27 0.03 0.19 0.33 0.19 0.01 0.02 0.01 43.86 M7 53.10 0.55 0.30 0.19 1.92 0.05 0.01 0.03 0.03 43.81 K1 55.57 0.10 0.02 0.01 0.37 0.16 0.01 0.04 0.01 43.71 K2 54.92 0.10 0.01 0.01 0.41 0.13 0.01 0.04 0.01 44.36 K3 54.80 0.22 0.01 0.01 0.40 0.11 0.01 0.04 0.01 44.39 K4 54.68 0.46 0.01 0.01 0.56 0.12 0.01 0.03 0.01 44.11 K5 54.37 0.75 0.01 0.01 0.35 0.14 0.01 0.04 0.01 44.31

K2O (%)

) P (%) WA (%) KH UCS (MPa) FS (MPa) IS (MPa) AR (cm3

T1 2640 1.52 1.38 113.38 54.56 7.92 17.00 24.01 T2 2650 1.46 1.24 117.96 55.25 8.09 19.00 23.48 T3 2660 1.28 1.06 122.54 56.85 8.46 21.00 23.05 T4 2670 1.15 0.94 126.28 57.94 8.89 22.00 22.61 T5 2680 1.04 0.87 129.35 58.65 8.95 23.00 22.04 M1 2690 0.96 0.82 131.14 59.85 9.03 24.00 21.79 M2 2700 0.88 0.78 135.76 62.16 9.28 25.00 19.95 M3 2705 0.75 0.66 137.89 64.85 9.46 26.00 19.01 M4 2710 0.71 0.55 141.52 66.85 9.86 27.00 18.72 M5 2715 0.68 0.43 143.78 68.75 9.98 28.00 18.13 M6 2720 0.66 0.38 145.78 70.45 10.12 29.00 17.79 M7 2730 0.52 0.32 155.45 77.04 10.94 31.00 17.58 K1 2735 0.38 0.28 168.25 84.10 12.85 33.00 17.29 K2 2745 0.25 0.21 173.56 87.25 13.94 34.00 16.57 K3 2755 0.23 0.18 178.24 90.84 14.96 36.00 16.05 K4 2775 0.20 0.16 184.58 93.26 16.24 38.00 15.34 K5 2800 0.16 0.14 190.95 97.08 18.45 40.00 14.12 D, density; P, porosity; WA, water absorption; KH, knoop hardness; UCS, uniaxial compressive strength; FS, flexural strength;

TiO2 (%)

P2O5 (%)

MnO (%)

LoI (%)

/50 cm<sup>2</sup> )

Statistical analysis of Cf of natural rocks depending on the dp and Va.

Figure 8 shows that there is a statistically significant relationship between Sc and Cf values. Correlation coefficient (R<sup>2</sup> ) values obtained from the natural rocks in the Fc at depths of cut of 1.2, 1.6 and 2.0 mm are 0.895, 0.871 and 0.859, respectively. Correlation coefficient (R2 ) values obtained from the natural rocks in the Ft at depths of cut of 1.2, 1.6 and 2.0 mm are 0.890, 0.878 and 0.880, respectively. Correlation coefficient (R2 ) values obtained from the natural rocks in the Fc at the Va of 2000, 2500 and 3000 mm/min are 0.771, 0.780 and 0.780, respectively. Correlation coefficient (R2 ) values obtained from the natural rocks in the Ft at the Va of 2000, 2500 and 3000 mm/min are 0.745, 0.781 and 0.781, respectively.
